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# The Fundamental Theorem of Calculus

# Change in Position Examples

### Example 1

A particle moving along the where is the particle when |

### Example 2

A cat climbing up and down a tree ends at height 3 feet after 10 seconds. If feet, how high in the tree was the cat
at time |

### Example 3

Let (a) If , that means we had to take 3 away from (b) If , that means we had to add 7 to |

### Example 4

A bicyclist is 10 miles from home after 3 hours of riding and 30 miles from home after 5 hours of riding. If her velocity is given by the function |

### Example 5

If |